Silicon-based modulator with optimized doping profile

ABSTRACT

A silicon modulator where the doping profile varies along the lateral and/or longitudinal position in the transition zones to achieve improved performance in terms of either optical attenuation or contact access resistance or both. A silicon-based modulator includes a waveguide including a contact region and a core region, wherein the waveguide includes a dopant concentration that decreases from the contact region to the core region in a transition zone according to a doping profile that is variable.

CROSS-REFERENCE TO RELATED APPLICATION(S)

The present disclosure is a continuation of U.S. patent application Ser.No. 16/666,830, filed Oct. 29, 2019 (now U.S. Pat. No. 10,983,369 whichissued on Apr. 20, 2021), which is also a continuation of U.S. patentapplication Ser. No. 16/609,239, filed Oct. 29, 2019, which is anational stage of PCT Application No. PCT/US19/015258, filed Jan. 25,2019, and entitled “SILICON-BASED MODULATOR WITH OPTIMIZED DOPINGPROFILES AND DIFFERENT TRANSITION ZONE THICKNESSES,” which claimspriority to U.S. Provisional Patent Application No. 62/622,494, filedJan. 26, 2018, and entitled “SILICON MODULATOR WITH OPTIMIZED DOPINGPROFILE AND REDUCED CONTACT RESISTANCE,” and to U.S. Provisional PatentApplication No. 62/712,659, filed Jul. 31, 2018, and entitled“SILICON-BASED MODULATOR WITH REDUCED CONTACT RESISTANCE,” the contentsof each are incorporated by reference herein.

FIELD OF THE DISCLOSURE

The present disclosure generally relates to optical communications. Moreparticularly, the present disclosure relates to a silicon-basedmodulator with an optimized lateral doping profile in a transitionregion, an optimized longitudinal doping profile in the transitionregion, and variable slab thickness in the transition region for reducedaccess resistance.

BACKGROUND OF THE DISCLOSURE

Silicon-based modulators are widely used in optical communicationsystems. It is well known in the art that silicon modulators can bebased on the use of a PN junction in a ridge waveguide. Such a waveguideis formed by providing a thick silicon waveguide core region (200 to 250nm thick, for example) surrounded by a thin slab (around 100 nm thick,for example). The PN junction is typically formed laterally by dopingone side of the waveguide with an N-type dopant, and the other side witha P-type dopant. The P and N regions are electrically connected onrespective sides to electrodes.

The doping concentration of the silicon in the waveguide core region hasto be weak, typically in the range of 1×10¹⁷ to 1×10¹⁸ cm⁻³, in order toavoid excessive optical loss. The doping concentration near theelectrodes has to be high, typically in the range of 1×10²⁰ to 1×10²¹cm⁻³, in order to permit a good ohmic contact to electrodes. On eachside of the PN junction, there is a transition zone connecting theweakly-doped region and the heavily-doped region. It is known in the artto use an intermediate doping level in the transition zone, forming athree-step profile, in order to adjust the compromise between opticalloss and contact resistance. One, two or three uniformly doped sectionsmay be used in this transition zone, see, for example, FIG. 1 . Each ofthese doped sections is uniform both in term of their vertical dopingconcentration profile and in term of the silicon waveguide geometry(e.g., height). Therefore, this doping profile is invariant within eachdoped section in the lateral direction (i.e., the direction between thejunction and each electrode) in the device.

BRIEF SUMMARY OF THE DISCLOSURE

In an embodiment, a silicon-based modulator (10) includes a waveguidecore (1) that is a PN junction region (12); a first transition zone (2)that is a P-side region (16) adjacent to the waveguide core (1) in alateral direction; a second transition zone (2) that is an N-side region(16) adjacent to the waveguide core (1) in a lateral direction and on anopposite side as the first transition zone (2); a first electricalcontact region (3) adjacent to the first transition zone (2); and asecond electrical contact region (3) adjacent to the second transitionzone (2), wherein at least one of the first transition zone and thesecond transition zone has a variation of doping concentration along alongitudinal direction. The variation of doping concentration can beformed by a plurality of areas of different doping concentrations in thelongitudinal direction. The variation of doping concentration can resultin one of lower optical losses for a given access resistance and loweraccess resistance for a given optical loss. The waveguide core can havea p-type doping of p and the first electrical contact has a p-typedoping of p++ such that the first transition zone has k (k≥2) divisionsP₁, P₂, . . . P_(k), each division effectively doped at a concentrationlevel p₁, p₂, . . . p_(k), respectively, such that p≤p₁<p₂ . . .<p_(k)≤p++, and the waveguide core can have an n-type doping of n andthe second electrical contact has an n-type doping of n++ such that thesecond transition zone has k (k≥2) divisions N₁, N₂, . . . N_(k), eachdivision effectively doped at a concentration level n₁, n₂, . . . n_(k),respectively, such that n≤n₁<n₂ . . . <n_(k)≤n++.

The variation of doping concentration can be different in the firsttransition zone (2) and the second transition zone (2). The variation ofdoping concentration can be periodic in the longitudinal direction. Thedoping concentration in the at least one of the first transition zone(2) and the second transition zone (2), adjacent to the correspondingelectrical contact region (3), can be equal therewith. The dopingconcentration in the at least one of the first transition zone (2) andthe second transition zone (2), adjacent to the waveguide core (1), canbe equal therewith. At least one of the first transition zone (2) andthe second transition zone (2) can have a variable thickness between thewavelength core (1) and the corresponding electrical contact region (3),wherein the variable thickness reduces access resistance relative to auniform thickness. The variation of doping concentration in alongitudinal direction can result in an effective lateral doping profilethat increases exponentially as a function of distance from thewavelength core (3). At least one of the first transition zone (2) andthe second transition zone (2) can have a variation of dopingconcentration along a lateral direction. A doping value in the variationof doping concentration along the lateral direction can have a maximumvalue of a doping value in the corresponding electrical contact region(3). A doping value in the variation of doping concentration along thelateral direction can have a maximum value of a doping value in thecorresponding electrical contact region (3). A doping value in thevariation of doping concentration along the lateral direction can bebetween a doping value in the wavelength core (1) to another dopingvalue in the corresponding electrical contact region (3).

In another embodiment, a silicon-based modulator (10) is obtained by aprocess including the steps of: determining an input profile for lateraldoping in a transition region (2) in the silicon-based modulator (10),the transition region is between a waveguide core (1) and an electricalcontact region (3), the input profile for the transition region (2) isuniformly doped in an optical propagation direction that is alongitudinal direction and has variation in doing along a lateraldirection; defining a number of implantation steps and associated dopantconcentrations; and, at each position along the lateral direction,determining an output profile dopant in the longitudinal direction suchthat its average is equal a dopant concentration of the input profile ata same lateral position.

In another embodiment, a silicon-based modulator with an optimizedlateral profile includes a waveguide core that is a PN junction region;a first transition zone that is a P-side region adjacent to thewaveguide core, the first transition zone has a first lateral dopingprofile; a second transition zone that is an N-side region adjacent tothe waveguide core on an opposite side as the first transition region,the second transition zone has a second lateral doping profile; a firstelectrical contact region adjacent to the first transition zone; and asecond electrical contact region adjacent to the second transition zone,wherein at least one of the first lateral doping profile and the secondlateral doping profile varies laterally from a first doping value in thewavelength core to a second doping value in the corresponding electricalcontact region. A doping value in one or more of the first lateraldoping profile and the second lateral doping profile can increaseexponentially as a function of distance from the wavelength core. Adoping value in one or more of the first lateral doping profile and thesecond lateral doping profile can have a maximum value of the seconddoping value in the corresponding electrical contact region. A dopingvalue in at least one of the first lateral doping profile and the secondlateral doping profile can be between the first doping value in thewavelength core to the second doping value in the correspondingelectrical contact region. One or more of the first lateral dopingprofile and the second lateral doping profile can be set based on loweroptical losses for a given access resistance or for lower accessresistance based on a given optical loss. The first lateral dopingprofile and the second lateral doping profile can be different.

In another embodiment, a silicon-based modulator with an optimizedlateral profile is formed by a process including the steps of:performing strong dopant implantation at a first electrical contactregion adjacent to a first transition zone and at a second electricalcontact region adjacent to a second transition zone; performing a longannealing process to both activate and diffuse ions in the firstelectrical contact region and the second electrical contact region;performing weak dopant implantation, relative to the strong dopantimplantation, at a waveguide core; and performing a short annealingprocess, relative to the long annealing process, to activate the weakdopant implantation, each annealing process includes an increase oftemperature for a short period of time that allows dopant ions tointegrate into a crystalline structure and become activated, wherein thelong annealing process and the short annealing process, in each of thefirst transition zone and the second transition zone, cause a dopingprofile from the wavelength core to the corresponding electrical contactregion that varies laterally.

In a further embodiment, a silicon-based modulator with an optimizedlongitudinal profile includes a waveguide core that is a PN junctionregion; a first transition zone that is a P-side region adjacent to thewaveguide core, the first transition zone has a first longitudinaldoping profile; a second transition zone that is an N-side regionadjacent to the waveguide core on an opposite side as the firsttransition region, the second transition zone has a second longitudinaldoping profile; a first electrical contact region adjacent to the firsttransition zone; and a second electrical contact region adjacent to thesecond transition zone, wherein the first longitudinal doping profilehas a variation of doping concentration along a longitudinal directionin the first transition region to mimic a first lateral doping profile.The silicon-based modulator of claim 1, wherein the first longitudinaldoping profile can be formed by uniformly-doped areas with differentshapes in the longitudinal direction. The first lateral doping profilecan be determined based on lower optical losses for a given accessresistance or for based on lower access resistance for a given opticalloss.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure is illustrated and described herein withreference to the various drawings, in which like reference numbers areused to denote like system components/method steps, as appropriate, andin which:

FIG. 1A illustrates a silicon modulator structure for a lateral PNjunction in accordance with one or more embodiments.

FIG. 1B illustrates a silicon modulator structure for a vertical PNjunction (sometime referred to by L-shaped junction) in accordance withone or more embodiments.

FIG. 1C illustrates a silicon modulator structure for a U-shaped PNjunction in accordance with one or more embodiments.

FIG. 2 illustrates a graphical illustration of a silicon waveguide,optical mode profile, and doping profile in accordance with one or moreembodiments.

FIG. 3 illustrates a flowchart for a method of fabricating a dopingprofile of a silicon-based modulator in accordance with one or moreembodiments.

FIG. 4 illustrates an optical modulator with an equivalent circuitillustrating resistance in accordance with one or more embodiments.

FIG. 5 illustrates the optical modulator illustrating optical losses inaccordance with one or more embodiments.

FIG. 6 illustrates a flowchart of an optimization process for thelateral doping profile in accordance with one or more embodiments.

FIG. 7 is a graph of resistivity versus impurity concentration for P andN-type dopants in accordance with one or more embodiments.

FIGS. 8A and 8B illustrate resistance per segment as a function ofoptical losses, for P and N-type dopants in accordance with one or moreembodiments.

FIG. 9 illustrates graphs of resistance per segment as a function ofoptical losses and doping in accordance with one or more embodiments.

FIG. 10 illustrates a cross-sectional view and a top view of asilicon-based modulator doping profile in accordance with one or moreembodiments.

FIGS. 11A-11D illustrate top-view examples of longitudinally varying thetransition zones of FIG. 10 in accordance with one or more embodiments.

FIG. 12 illustrates an optical modulator 10 various longitudinallyvarying doping profiles (Z-axis) in accordance with one or moreembodiments.

FIGS. 13A and 13B illustrate a graph of an initial N dopant profile anda top view of an optical modulator associated therewith in accordancewith one or more embodiments.

FIGS. 14A, 14B, and 14C illustrate diagrams of various longitudinallyvarying profiles in accordance with one or more embodiments.

FIG. 15 illustrates a graph of depletion width as a function of voltagefor the three embodiments of FIGS. 14A, 14B, and 14C.

FIG. 16 illustrates a top view of an optical modulator and an equivalentcircuit in accordance with one or more embodiments.

FIG. 17 illustrates an example embodiment with a stepwise profile as theinput profile and an output profile with two implantation steps inaccordance with one or more embodiments.

FIG. 18 illustrates a diagram of the output profile from the inputprofile of FIG. 17 in accordance with one or more embodiments.

FIG. 19 illustrates a graph of the response of an RC filter with acut-off frequency of 80 GHz, 100 GHz, and 120 GHz in accordance with oneor more embodiments.

FIGS. 20A, 20B, and 20C illustrate three PN junctions with varyinglongitudinal profiles in accordance with one or more embodiments.

FIG. 21 illustrates a graph of time versus bias voltage for the chargecarrier concentration simulation of the three PN junctions in FIGS. 20A,20B, and 20C in accordance with one or more embodiments.

FIG. 22 illustrates a graph of the average depletion width profile as afunction of time for the PN junction of FIG. 20A in accordance with oneor more embodiments.

FIG. 23 illustrates a graph of the average depletion width profile as afunction of time for the PN junction of FIG. 20B in accordance with oneor more embodiments.

FIG. 24 illustrates a graph of the average depletion width profile as afunction of time for the PN junction of FIG. 20C in accordance with oneor more embodiments.

FIGS. 25A and 25B illustrate a first example embodiment with an inputprofile and output profile in accordance with one or more embodiments.

FIGS. 26A and 26B illustrate a second example embodiment with an inputprofile and output profile in accordance with one or more embodiments.

FIGS. 27A and 27B illustrate a third example embodiment with an inputprofile and output profile in accordance with one or more embodiments.

FIGS. 28A and 28B illustrate a fourth example embodiment with an inputprofile and output profile in accordance with one or more embodiments.

FIGS. 29A and 29B illustrate a fifth example embodiment with an inputprofile and output profile in accordance with one or more embodiments.

FIGS. 30A and 30B illustrate a sixth example embodiment with an inputprofile and output profile in accordance with one or more embodiments.

FIG. 31 illustrates a top view of another embodiment of a longitudinallyvarying profile in accordance with one or more embodiments.

FIGS. 32A and 32B illustrate graphs of N (FIG. 32A) and P (FIG. 32B)dopants illustrating optical losses as a function of resistance persegment in accordance with one or more embodiments.

FIGS. 33A and 33B illustrate a single mode silicon modulator withvarying transition zone thickness in accordance with one or moreembodiments.

FIGS. 34A and 34B illustrate a multimode silicon modulator with varyingtransition zone thickness in accordance with one or more embodiments.

FIGS. 35-38 illustrate cross-sectional diagrams of various modulatorswith the waveguide core and the transition regions and associatedcalculated optical mode illustrating different slab thicknesses in thetransition regions in accordance with one or more embodiments.

FIG. 39 illustrate graphs of a full modulator simulation forillustrating different slab thicknesses in the transition regions inaccordance with one or more embodiments.

DETAILED DESCRIPTION OF THE DISCLOSURE

Embodiments disclosed herein relate to design of a silicon-basedmodulator. Specifically, embodiments disclosed herein describe a novelsilicon modulator where the doping profile varies along the lateraland/or longitudinal position in the transition zones to achieve improvedperformance in terms of either optical attenuation or contact accessresistance or both. In embodiments disclosed herein, the siliconmodulator may include a waveguide having a core and a transition zonebetween the core and electrodes on either side of the waveguide, wherethe shape of the transition zone is varied to achieve an improvedperformance. The shape of the transition zone may include, for example,a height (i.e., a thickness) of the transition zone. As describedherein, access resistance describes the resistance between the externalworld and the modulating PN junction (waveguide core).

Although silicon is the material widely used in modulators for opticalcommunications, it would be readily appreciated by one skilled in theart that the subject matter disclosed in this document may be applicableto modulators based on other semiconductor materials.

FIG. 1 provides cross-section views of three typical silicon modulators,each with a different PN junction shape. It would be readily appreciatedby one skilled in the art that in addition to these three types of PNjunctions, there may be other types of PN junctions used in the siliconmodulator disclosed herein, without departing from the presentdisclosure.

While the doping concentration in each of the transition zones in FIG. 1is uniform (N+ and P+ respectively), FIG. 2 shows a novel, non-uniformdoping profile in the transition zones 2 to achieve optimum trade-offbetween optical attenuation and contact resistance, wherein x representsthe position in the transition zone 2 between the NP junction and eachside electrode and N(x) represents the doping level at a given position.For illustration purposes, only the electrode on p-side is shown in FIG.2 .

First, consider the optical attenuation. Let η(x) express the lateraloptical mode intensity profile. As seen in FIG. 2 , in one or moreembodiments, because the focus is on the transition zone 2, the originof this profile is set at the beginning of the transition zone 2 insteadof the middle of the waveguide. Although the mode is mainly contained inthe waveguide core 1 defined by the thick portion of the ridgewaveguide, there may be some light that extends in the slab region. Theintensity of light at a given position in the slab region decreasesexponentially as the distance from the waveguide core 1 grows.

Accordingly, in the transition zone 2, the mode profile may beapproximated as:

$\begin{matrix}{{{\eta(x)} = {{\eta(0)}e^{{- \beta}x}}}.} & (1)\end{matrix}$

The fraction of the mode energy at position x and over a width dx isgiven by:

$\begin{matrix}{{{d{\eta(x)}} = \frac{{\eta(x)}dx}{\int_{- \infty}^{\infty}{\eta(x)}}}.} & (2)\end{matrix}$

The presence of free carriers creates an absorption of light. Accordingto the well-known Soref equations (such as described in R. Soref and B.Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron.,vol. 23, no. 1, pp. 123-129, 1987, the contents of which areincorporated by reference), there is a linear dependency between theattenuation coefficient and the free carrier concentration. Since thefree carrier concentration equals the dopant concentration, one canconsider that the attenuation contribution at the position x is directlyproportional to the dopant concentration at this location and to thefraction of the mode energy at this same location:

$\begin{matrix}{{{d{\alpha(x)}} = {{A \cdot {N(x)} \cdot d}{\eta(x)}}},} & (3)\end{matrix}$

where A is a constant.

The overall mode energy can be considered as a constant. Thus, the sameequation may be written as:

$\begin{matrix}{{d{\alpha(x)}} = {d{A \cdot {N(x)} \cdot {\eta(x)}}}} & (3)\end{matrix}$

where dA is another constant.

If the focus is on the contribution of the attenuation only at locations0 and x, consider that they together provide attenuation of:

$\begin{matrix}{{d{\alpha\left( {0,x} \right)}} = {{dA} \cdot {\left( {{{N(0)} \cdot {\eta(0)}} + {{N(x)} \cdot {\eta(x)}}} \right).}}} & (4)\end{matrix}$

From that condition, a perturbation may be considered where the dopingconcentration is slightly changed by an amount ΔN₀ at 0 and ΔN_(x) at x.The attenuation contribution becomes:

$\begin{matrix}{{d{\alpha\left( {0,x} \right)}^{\prime}} = {d{A \cdot {\left( {{\left( {{N(0)} + {\Delta N_{0}}} \right) \cdot {\eta(0)}} + {\left( {{N(x)} + {\Delta N_{x}}} \right) \cdot {\eta(x)}}} \right).}}}} & (5)\end{matrix}$

Considering the last two equations, one of ordinary skill in the artwould readily appreciate that the attenuation remains unchanged if:

$\begin{matrix}{{{{\Delta{N_{0} \cdot {\eta(0)}}} + {\Delta{N_{x} \cdot {\eta(x)}}}} = 0},} & (6)\end{matrix}$

or in other words if:

$\begin{matrix}{{\Delta N_{x}} = {{- \Delta}N_{0}{\frac{\eta(0)}{\eta(x)}.}}} & (7)\end{matrix}$

Now consider the contact resistance. The sheet resistance of a thinlayer of doped silicon decreases as the doping concentration increases.It is experimentally found that, within a certain range of interest, thesheet resistance R depends on the doping concentration N as:

$\begin{matrix}{{R = {KN^{- \gamma}}},} & (8)\end{matrix}$

where K is a constant and γ found to be about 0.7.

The contact resistance of the modulator is the sum of infinitesimalsheet resistances between the electrode and the waveguide.

Again, focusing only at contributions at 0 and x, an equation may bewritten as:

$\begin{matrix}{R_{0,x} = {{K{N(0)}^{- \gamma}} + {K{{N(x)}^{- \gamma}.}}}} & (9)\end{matrix}$

Now consider the change in the contact resistance resulting from achange in the doping concentration at 0 and x with the amounts alreadyintroduced:

$\begin{matrix}{R_{0,x}^{\prime} = {{K\left( {{N(0)} + {\Delta N_{0}}} \right)}^{- \gamma} + {{K\left( {{N(x)} + {\Delta N_{x}}} \right)}^{- \gamma}.}}} & (10)\end{matrix}$

With ΔN_(x) chosen to keep the optical attenuation unchanged, theequation is:

$\begin{matrix}{R_{0,x}^{\prime} = {{K\left( {{N(0)} + {\Delta N_{0}}} \right)}^{- \gamma} + {{K\left( {{N(x)} - {\Delta N_{0}\frac{\eta(0)}{\eta(x)}}} \right)}^{- \gamma}.}}} & (11)\end{matrix}$

For a small value of ΔN₀, the equation becomes:

$\begin{matrix}{R_{0,x}^{\prime} \approx {{{KN}(0)}^{- \gamma} + {K{N(x)}^{- \gamma}} + {\Delta N_{0}K\gamma\left\{ {{\frac{\eta(0)}{\eta(x)}{N(x)}^{{- \gamma} - 1}} - {N(0)}^{{- \gamma} - 1}} \right\}} + {\Delta N_{0}^{2}\frac{K{\gamma\left( {\gamma + 1} \right)}}{2}{\left\{ {{\left( \frac{\eta(0)}{\eta(2)} \right)^{2}{N(x)}^{{- \gamma} - 2}} - {N(0)}^{{- \gamma} - 2}} \right\}.}}}} & (12)\end{matrix}$

When the term that is linear as ΔN₀ vanishes, that is when:

$\begin{matrix}{{{{\frac{\eta(0)}{\eta(x)}{N(x)}^{{- \gamma} - 1}} - {N(0)}^{{- \gamma} - 1}} = 0},} & (13)\end{matrix}$the contact resistance necessarily increases regardless of the value andthe sign of □N₀. In other words, in one or more embodiments, the dopingprofile is optimum when the above equation is met, as being the one thatprovides the lowest contact resistance.

The doping concentration at position x can be isolated from the equation(13) above, thus providing an expression for the optimum doping profile:

$\begin{matrix}{{{N(x)} = {{N(0)}\left( \frac{\eta(0)}{\eta(x)} \right)^{\frac{1}{\gamma + 1}}}}.} & (14)\end{matrix}$

For a modal profile given by equation (1), one has the optimum lateraldoping profile given by:

$\begin{matrix}{{N(x)} = {{N(0)}{e^{{(\frac{\beta}{\gamma + 1})}x}.}}} & (15)\end{matrix}$

Based on the above and as illustrated in FIG. 2 , it may be seen thatthe doping profile N(z) tends to increase exponentially as a function ofthe distance from the waveguide core 1. In one or more embodiments, ahigher limit may be placed to the doping concentration N_(max), beingthe one selected for the ohmic contact 3 near the electrode. If such amodification is performed, a profile such as that illustrated at thebottom of FIG. 2 may be achieved.

During fabrication, doping is achieved by bombarding the surface of thesilicon with dopant ions. As in many steps of CMOS fabrication, thisimplantation is done only at certain locations by using a mask. Afterimplantation, the ions are interstitial in the material and does notprovide the desired dopant effect of providing or capturing freecarriers.

In order to provide the desired dopant effect, the dopants are requiredto be integrated within the crystalline structure. In one or moreembodiments, an annealing process involving an increase of temperaturefor a short period of time allows the dopant ions to integrate into thecrystalline structure and become activated.

The annealing process not only activates the dopants but also allowsthem to diffuse in their vicinity. This diffusion causes a blurring ofthe initial dopant distribution both in depth and laterally away fromthe mask edge.

By choosing an appropriately long time annealing process, it is possibleto obtain a dopant profile close to the optimum one illustrated in FIG.2 .

In one or more embodiments, the dopant distribution within the waveguidecore 1, that is, the one that forms the PN junction, is required to beas sharp as possible and dopant distribution at this location isrequired to diffuse as little as possible during the annealing process.To achieve both a smooth profile in the transition zone 2 and a sharpprofile in the waveguide core 1, the fabrication method P1 described inFIG. 3 may be performed.

In a first step S1, a first strong implantation is performed in theelectrode regions 3.

In a second step S2, a long annealing is performed to both activate anddiffuse the ions of the first step implantation.

In a third step S3, a second weak implantation is performed in thewaveguide core region 1.

In a fourth step S4, a second short annealing is performed to activatethe second weak implantation while keeping its diffusion as low aspossible.

In one or more embodiments, the method of FIG. 3 and the equationsdescribed above may be used to calculate an optimum lateral dopingprofile in the transition zones 2 between the waveguide core 1 and theelectrodes of the silicon modulator. In addition, embodiments alsorelate to the fabrication of one or more silicon modulator deviceshaving a doping profile that approaches the calculated optimum profilein accordance with the above description. As described herein, lateralmeans the direction from the wavelength core 1 to the electrode regions3. That is, the doping profile in the transition regions 2 is variedfrom the waveguide core 1 to the electrode regions 3 in a lateraldirection, i.e., from right to left or left to right looking at FIG. 1 .Conversely, the longitudinal direction would be into the page.

Optimizing the Lateral Doping Profile

A quantitative evaluation of the optimal doping profile is nowdescribed. FIG. 4 illustrates an optical modulator 10 with an equivalentcircuit illustrating resistance and FIG. 5 illustrates the opticalmodulator 10 illustrating optical losses. Again, the optical modulator10 includes three sections, namely a PN junction region 12, anelectrical contact region 14, and a transition region 16. The PNjunction region 12 region is where an optical wave accumulates a phaseshift due to the PN junction. The electrical contact region 14 is wherean electrical signal applied to the optical modulator 10 istransitioning from a doped silicon layer to a metal via. The transitionregion 16 is between the PN junction region 12 and the electricalcontact region 14. The position of the transition region 16 can varydepending on the PN junction geometry. For example, the siliconthickness of the slab in the transition region 16 can be around 90 nm.

In various embodiments, optimization is described for the two transitionregions 16. As described herein, an optimized lateral doping profileprovides lower optical losses for a given access resistance or viceversa. The electrical circuit of a depletion-based modulator is shown inFIG. 4 where R_(contact) is the contact resistance, R_(trP) and R_(trN)is the resistance associated to the transition regions and R_(pn) anC_(pn) are the resistance and capacitance of the PN junction region. Thetotal resistance of the phase shifter (the PN junction region 12) isgiven by 2R_(contact)+R_(pn)+R_(trP)+R_(trN). However, in the context ofoptimizing the lateral doping profile, only the contribution of R_(trP)and R_(trN) are considered. The lateral doping profile does not have animpact on the contact resistance nor on the resistance in the PNjunction.

As a reference for comparison, resistances were measured in an opticalmodulator 10 with a conventional doping profile. The resistances weremeasured experimentally as R_(contact)˜2.5Ω, R_(pn)˜12Ω, R_(trp)˜26Ω,and R_(trN)˜15Ω for segments that were 150 microns in length. Thus, thelateral doping profile is a significant contributor of the totalresistance the PN junction region 12.

Referring to FIG. 5 , the optical losses (OL) were simulated andconfirmed experimentally and can be decomposed into: 1) Sidewallroughness loss, 2) loss in the PN junction regions, 3) loss on the Pside, and 4) loss on the N side. These values in the physical opticalmodulator 10 are as follows: 1) Sidewall roughness loss ˜2 dB/cm—loss ofthe waveguide without implantation. This loss comes from the overlap ofthe optical mode width the rough sidewalls of the waveguide. 2) The lossin the PN junction region (biased at the typical operating point of 2V)˜3.8 dB/cm (the largest portion of the mode intensity). 3) Loss on theP side˜0.8 dB/cm. 4) Loss on the N side˜1.1 dB/cm. A large portion ofthe optical losses is from the dopants in the PN junction region 12.However, the propagation loss in the access regions is not negligible.

FIG. 6 is a flowchart of an optimization process P2 for the lateraldoping profile. In a first step S11, a target resistance is provided asa condition for the convergence.

In a second step S12, the optimization process minimizes the opticallosses for this specific resistance value.

In a third step S13, the concentration profile is bounded. A maximaldoping concentration is defined (corresponding to the dopingconcentration required at the electrical contact region). A minimaldoping concentration is also defined (this value is not necessarilydetermined by the PN junction region doping concentration, but thisvalue is swept).

In a fourth step S14, the optical mode of the various optical waveguidegeometries is simulated, such as in a Lumerical Mode solution, and thedopants are considered as a perturbation. As a result, the simulatedstructures do not contain dopants. The optical losses are calculatedafterward using the overlap of the unperturbed mode on the doped areas.The complex effective index of the doped regions is obtained using Sorefequations. The vertical doping profile is considered uniform.

In a fifth step S15, the optimization of the lateral profile isperformed independently for P and for N.

In a sixth step S16, the resistivity of the doped silicon region isobtained using the well-known empirical results, e.g., FIG. 7 is a graphof resistivity versus impurity concentration for P and N-type dopants.

As mentioned herein, an optimal lateral profile is calculated using atarget resistance value (the OL is minimized). Once the profile isfound, the optimal OL is calculated for this specific resistance value.To evaluate the impact of optimizing lateral profiles, a series ofprofiles were calculated with various target resistance values (from 5to 30Ω).

FIGS. 8A and 8B illustrate resistance per segment as a function ofoptical losses, for P and N-type dopants. The open dots representexperimental data of actual modulators while the black dots are thesimulated results for the same modulator. The difference between theblack and open dots can be associated with an error in the fabricationprocess or an error in the experimental characterization of the OL/Rparameters. However, the close proximity of these two points does notmodify the main conclusion. The “x” markers correspond to a modulatorusing the optimal doping profile and having the same OL as theexperimental modulator.

The top figure of FIG. 9 is the same curve as shown in FIG. 8A (for Ponly). The bottom figures of FIG. 9 are the optimized lateral profiles(linear (left graph) and log scale (right graph)) for various values ofaccess resistance (indicated by the markers in the top figure). Asdiscussed herein, the optimal profiles indeed follow an exponentialshape.

The potential gain for this technique is between 12-16Ω for a single PNjunction.

In an embodiment, modulators can be series push-pull (SPP) which includetwo diodes back to back. As a result, the total capacitance of thecircuit is halved, and the resistance is twice the one shown previously.Thus, the improvement is doubled.

The improvement of 12-16Ω for one PN junction or 24-32Ω for an SPPmodulator results in a bandwidth improvement of about 4-5 GHz (suchimprovement was simulated based on the experimental data provided hereinfor the experimental modulator).

Thus, the benefit of this approach is significant since it increases thebandwidth without degrading any other parameters. Furthermore, thenon-optimal lateral profiles conventionally used are more likely toproduce an imbalance in the loss of the Mach-Zehnder modulator (MZM)arms because of potential mask misalignment, and thus degradation of theExtinction Ratio (ER) of the Mach-Zehnder Interferometer (MZI).

Longitudinal Profile

While the doping profile according to the equation (15) is achievablethrough the aforementioned fabrication method, one or more embodimentsdiscussed herein relate to mimicking such a lateral doping profile inthe aggregate, in which the doping concentration gradually changes alongthe longitudinal direction, using configurations of uniformly-dopedareas with different shapes. Indeed, the attenuation of the lightpropagating through the waveguide is the sum of the attenuationexperienced through the many longitudinal sections. The overallattenuation is then equivalent to the longitudinal average of thelateral doping profile. In the same manner, the contact resistancedepends on the full geometric dopant profile.

The following discussion provides examples in which such a lateraldoping profile may be achieved, via changes along the longitudinaldirection, using configurations of uniformly-doped areas with differentshapes. The following discussion focuses on the configuration of thetransition zone 2, which exists between the region 1 where the opticalmode is confined and each electrode. In the transition zone 2, theoptical mode is exponentially decaying. The transition zone 2 has adominating influence on the performance of optical modulators. Highdoping concentrations will result in modulators with high optical lossesbut with good modulation bandwidth, whereas low doping concentrationwill produce modulators with low optical losses but with reducedbandwidth.

In one or more embodiments, in a first example, instead of uniformlydoping a slab-shaped transition zone 2, e.g., a slab-shaped p-typetransition zone, at concentration level p+ whereas p<p+<p++, p being theconcentration level of the P region 1 on the P side of the PN junctionand p++ being the concentration level at the P++ region 3 contacted bythe anode, one may divide such p-type transition zone 2 into k (k≥2)divisions P₁, P₂, . . . P_(k) arranged in order along the longitudinaldirection, each division uniformly doped at a concentration level p₁,p₂, . . . p_(k), respectively, such that p≤p₁<p₂ . . . <p_(k)≤p++,wherein the weakest doped division P₁ is adjacent to the P region 1 andthe most heavily doped division P_(k) is adjacent to the P++ region 3and wherein the boundary between two adjacent divisions meanders alongthe direction of wave propagation. Also, the same holds for the ntransition region, using n, n+, n++, N₁, N₂, etc. Further, an arbitrarylongitudinal doping profile effect may be achieved using regions ofuniform doping. In addition to the lateral doping profile optimization,the present disclosure includes providing, on each side of the opticalmodulator 10, a transition zone 2 having two regions of uniform dopingconcentration, but non-uniform width as a function of the longitudinalposition.

An example of such a doping profile is shown in FIG. 10 in accordancewith one or more embodiments disclosed herein. Specifically, FIG. 10illustrates an example scenario of dividing the transition zone 2 into 2divisions (k=2) and shows a transition zone 2 that includes an aperiodicpattern. As seen in FIG. 10 , the transition zones 2 include two dopingconcentrations p1 and p2 on the p side, and two doping concentrations n1and n2 on the n side.

Again, the aim of the transition zone 2 is to provide a trade-offbetween low optical loss and low access resistance. The dopingconcentration in this region is required to be as high as possible inorder to provide a low access resistance which is needed to achieve ahigh modulation bandwidth. However, it is also required to be as low aspossible to provide a low optical loss. The optical mode is mainlycontained within the waveguide core (the thick portion of the ridgewaveguide) but also extends in the slab region, typically in the form ofexponential decay.

For an optimum trade-off, the doping concentration in the transitionzone is required to continuously increase in a specific way from thewaveguide to the electrode region, as described herein. However,providing specific spatially-dependent doping concentration is not easyto obtain in practice due to the typical fabrication lithographyinvolving illuminating through a mask. Such a binary method is rathermore suited for the fabrication of uniformly doped sections.

The longitudinal dependence of the doping width allows mimicking alateral doping profile. Indeed, the attenuation of the light propagatingthrough the waveguide is the sum of the attenuation experienced throughthe many longitudinal sections. The overall attenuation is thenequivalent to the longitudinal average of the lateral doping profile. Inthe same manner, the access resistance depends on the full geometricdopant profile.

FIGS. 11A-11D further provide four variations of possible meanderingboundaries between P₁ and P₂ for two divisions (k=2). As can be seen inFIGS. 11A-11D, each of the longitudinally varying transition zones has adifferent geometry/shape. Specifically, FIG. 11A shows a transition zonethat mimics three doping levels but is based on the use of only twolevels. FIG. 11B shows a transition zone that includes a lineartransition between the two doping levels. FIG. 11C shows a transitionzone that includes a non-linear transition between the two dopinglevels. FIG. 11D shows a transition zone that includes a non-lineartransition between the two doping levels using an interleaving strategyto minimize local non-uniformities and/or large pattern period.

Nevertheless, it would be readily appreciated by one skilled in the artthat FIGS. 11A-11D is not an exhaustive list of possible boundarypatterns. Other possible patterns may include zigzag, sinusoidal, or thecombination thereof, and may be aperiodic along the direction of wavepropagation. It would also be readily appreciated by one skilled in theart that the shapes of the divisions may be different, and the sizes ofthese divisions may not necessarily be the same.

In one or more embodiments, the longitudinally varying transition zone 2may include one or more of the following characteristics:

The longitudinally varying doping profile may be periodic or aperiodic;

The doping concentrations p₁ and p may be equal;

The doping concentrations p₂ and p++ may be equal;

The doping concentrations n₁ and n may be equal;

The doping concentrations n₂ and n++ may be equal; and

The longitudinally varying doping profile may be chosen such that itslongitudinal average agrees with the optimum lateral doping profile.

In one or more embodiments, an annealing process may be advantageouslyused after implantation of the longitudinally varying doping in order toblur the spatial distribution and tend to a smooth spatially-varyingprofile.

The longitudinally varying doping profile in the transition zones 2 maybe such that the electric field within the PN junction containsvirtually no longitudinal variation. The P and N regions 1 in thewaveguide would thus act as a damping zone sufficient to provide alongitudinally uniform depletion of the PN junction.

The first example described above allows for fabricating siliconmodulators with improved performance. Due to the flexibility provided inthe fabrication, embodiments described in the first example allow alateral profile that optimizes the trade-off between optical loss andcontact resistance to be easily obtained. More specifically, for a givenacceptable optical loss, a modulator having a lower contact resistancemay be obtained, which translates into a higher bandwidth device.

Reproducing a Custom Lateral Profile with a Longitudinal Profile

Again, a custom lateral implantation profile could be implemented usinga longitudinal variation of the dopant. Typically, the doped regions ofan optical modulator are fabricated by patterning a photoresist layerusing a photolithographic mask and doing the implantation with ions ofspecific energy, dose, and angle, followed by rapid thermal reflow. Thisleads to the integration of impurities into the silicon lattice withconcentrations (in principle) uniformly distributed along the XZ axis(where the photoresist was removed) while avoiding such impurities wherethe silicon was protected by the photoresist. The implantation profilealong the Y direction depends on the implantation recipe and is assumedto have a uniform doping concentration. The repetition of such process(with various implantation recipes and different masks) will typicallycreate stepwise implantation profile.

FIG. 12 illustrates an optical modulator 10 with various longitudinallyvarying doping profiles (Z-axis). In an embodiment, any lateral dopingprofile (X-axis) (also referred to as input profiles) (e.g., stepwise(line 20) or continuous (line 22)) can be effectively achieved usinglongitudinally varying profiles (Z-axis) (also referred to herein asoutput profiles, as our optimization works to determine the appropriateoutput profile based on the desired input profile). The allowsfabrication of elaborate dopant profiles with fewer implantation steps(the masks are shown in shading) and without custom annealing time.These input profiles are uniform in the optical propagation direction(Z-axis) and in the vertical axis (Y-axis) (top-left figure) while theoutput profiles are varying in the Z-direction.

The three main figure of merits (FOM) of optical modulators are 1)Optical losses, 2) Vπ, and 3) Electrical/Optical (EO) bandwidth. Tovalidate the relevance of the embodiments described herein, it isnecessary to properly characterize its impact on the modulator FOMs.FIGS. 13A and 13B illustrate a graph of an initial N dopant profile anda top view of an optical modulator 30 associated therewith.

When the lateral profile (i.e., the input profile) is converted into alongitudinal profile (i.e., the output profile), it is desired that theoptical losses of both the input and the output profiles remain thesame. To ensure that this will be true, the following process includes:

1. The input profile is defined (e.g., graph in FIG. 13A). This profilecan be based on the optimizations described herein for lateral profiles.

2. The number of implantation steps (and their dopant concentrations) isdefined (three implantation steps are presented in this example) (dottedlines 32, 34 in FIG. 13A are given for dotted line 36 in FIG. 13B on theN side of the waveguide).

3. At each position along the X-axis (dotted line 36 in FIG. 13B), theoutput profile dopant in the Z-direction is determined such that itsaverage is equal to the dopant concentration of the input profile at thesame X-position (black circle). Since the propagation losses (dB/cm)associated to dopant implantation is linearly proportional to theconcentration density, the losses in both profiles will thus be equal.

FIGS. 14A, 14B, and 14C are diagrams of various longitudinally varyingprofiles. In principle, the V_(π) should not be influenced by the accessresistance because, in a PN junction operated with a reverse bias, thereis no current flowing. As a result, any point on a given side of the PNjunction (on the X and Z-axis) is at the same potential. To confirm thisstatement, DC simulations as a function of voltage were made for the PNjunctions shown in FIGS. 14A, 14B, and 14C. One PN junction is uniform(FIG. 14A), the second has a moderately doped teeth (FIG. 14B), and thethird one has heavily doped teeth (FIG. 14C).

The depletion width as a function of voltage for the three simulationsis shown in the graph of FIG. 15 . The three curves for the embodimentsof FIGS. 14A, 14B, and 14C actually superimpose each other in the graphof FIG. 15 , showing that the access resistance does not influence themodulator DC V_(π).

To evaluate how the longitudinal profile affects the bandwidth of amodulator, consider the EO response of an optical modulator, which isgiven by [16] which was taken from G. L. Li, T. G. B. Mason, and P. K.L. Yu, “Analysis of Segmented Traveling-Wave Optical Modulators,” J.Lightwave Technol., JLT, vol. 22, no. 7, p. 1789, July 2004, thecontents of which are incorporated by reference herein:

$\begin{matrix}{{E{O(f)}} = {{❘{\frac{2}{NV_{s}}\sum\limits_{n = 1}^{N}}❘}V_{n}{{❘{e^{\Delta\phi}\frac{1}{1 - {i\omega RC}}}❘}^{2}.}}} & (16)\end{matrix}$Aside of the term 2/NV_(s), which is only a normalization constant, theEO response of an optical modulator is decomposed into three terms.

1) the term V_(n) is the voltage appearing at the segment n (see FIG. 16which is a top view of an optical modulator is and an equivalentcircuit). The curve V_(n) vs. segment number (or versus position alongthe modulator) represents the Radio Frequency (RF) losses accumulated inthe modulator (which is the dominant term in the EO response of a SiPmodulator). If the averaged resistance of segment N−1 remains the same,the voltage at the next segment (V_(n)) will not change.

2) e^(Δϕ) is a phase term that takes into account the velocity mismatchbetween the RF and the optical wave. For a PN junction having arelatively low capacitance, the resistance of the junction does not havea significant impact on the RF velocity. Thus, this term will not changewith a reduction/increase of the access resistance. Furthermore, in theevent that the resistance has an impact on the RF velocity, the RFwaveguide design could be slightly modified to compensate for thiseffect. Finally, in the case where the access resistance of the outputprofile is the same as the input profile one, this term will be exactlythe same. To conclude, this term does not play a role.

3) The third term

$\left( \frac{1}{1 - {i\omega RC}} \right)$comes from the Resistor-Capacitor RC response of the PN junction of onesegment. To illustrate the impact of having a longitudinal variation ofthe doping profile, FIG. 17 illustrates an example embodiment with astepwise profile as the input profile 40 and an output profile with twoimplantation steps. Typical resistance and capacitance value are shownin FIG. 17 . Typical PN junctions have an RC cut off frequency of thisjunction is thus close to 100 GHz. The baseline PN junctions withoutintermediate dopant have a resistance of about 13.5 □/mm. The bandwidthis thus close to 80 GHz.

FIG. 18 illustrates a diagram of the output profile from the inputprofile 40 of FIG. 17 . The analysis can be simplified by evaluating theRC constant of three uniform sections 50, 51, 52 separately. In thissituation, the central section 50 will have an access resistance (in□/mm) smaller than the input profile whereas the side sections 51, 52will have an access resistance larger than the input profile. Since thecut-off frequency of the modulator is relatively large compared totypical 3 dB bandwidth of depletion-based silicon modulator, this effecthas only a minor impact on the overall bandwidth. A graph in FIG. 19illustrates the response of an RC filter with a cut-off frequency of 80GHz, 100 GHz, and 120 GHz. The RC filter thus has an impact of about 0.5dB at 40 GHz, and the variation is coming from the longitudinal profileis about 0.25 dB. To conclude, at high frequencies, the PN junction inthe section 51, 52 will open slightly less the PN junction in section50. However, this effect is negligible compared to the impact of V_(n)on the modulator bandwidth.

To validate the discussion above, charge carrier simulations wereperformed on three PN junctions 61, 62, 63 illustrated in FIGS. 20A,20B, and 20C. The PN junction 61 has a uniform longitudinal profile. ThePN junction 62 has a stepwise longitudinal profile. In this example,there is a longitudinal profile (a tooth), but the cut-off frequency ineach of the regions are much larger than the modulator bandwidth. The PNjunction 63 has a stepwise longitudinal profile with fully etched accessregions. In this example, the silicon has been fully removed from theside of the tooth (hatched zone) to increase drastically the resistanceof the side of the junction.

In these embodiments, the charge carrier concentration was simulatedwith a time-varying bias voltage. The simulation was done over twoperiods of a 40 GHz applied signal. FIG. 21 is a graph of time versusbias voltage for the charge carrier concentration simulation. The chargecarriers around the optical waveguide are going to be shown at the timestep indicated by a marker 70. The average depletion width (averagedover the full PN junction) is also going to be displayed as a functionof time as follows.

FIG. 22 illustrates a graph of the average depletion width profile as afunction of time for the PN junction 61 of FIG. 20A. As expected, inthis situation, it is seen that the depletion region is uniformly openedalong the waveguide (arrows 71). The P dopant (positive) are on the leftwhile the N dopant is on the right. The average depletion width profileis presented as a function of time.

FIG. 23 illustrates a graph of the average depletion width profile as afunction of time for the PN junction 62 of FIG. 20B. In this situation,it is seen that the depletion region is uniformly opened along theposition although there is a longitudinal doping profile. The cut-offfrequencies are large enough for the various regions such that theopening of the depletion region at 40 GHz seems uniform. The averagedepletion width profile as a function of time is identical to the onepresented in FIG. 22 .

FIG. 24 illustrates a graph of the average depletion width profile as afunction of time for the PN junction 63 of FIG. 20C. In this situation,it is seen that the depletion region is not uniform along the positionbecause the RC filter in the outer region is very large. The PN junctionopens only in the center (circle 72) where the access silicon slab isnot fully etched. The average depletion width is thus much smaller thanthe two precedent cases (i.e., the depletion width is not modulated onthe side and varies only in the center). Note that the opening of thedepletion region at the center is exactly the same as in the twoprevious cases. These simulations prove that the discussion on theimpact of the longitudinal profile on the EO response is valid.

Implementing a laterally varying dopant profile into a longitudinallyvarying profile is relevant because

The optical losses remain the same;

The DC Vπ is not influenced by the access resistance of the junction.Thus the DC Vπ is also not changed; and

The EO bandwidth is also very similar. As mentioned before:

From a macroscopic point of view, if the total resistance of the outputprofile is equal to the input profile, the RF loss will be identical(i.e., the terms Vn will be identical).

From a microscopic point of view, the RC filter equation of each segmentwill be slightly affected by the longitudinal variation of the dopant.Some areas have lower access resistance than some other areas. However,this effect is negligible in the case that interests us (where the RCcut-off frequency>>modulator bandwidth). Thus, for an equivalentresistance, the EO bandwidth of a longitudinally varying profile remainsthe same.

To evaluate the resistance of a longitudinal profile, the dopant P and Nare calculated independently. Each profile is separated into M sectionsin the Z-axis, and the resistance is calculated considering each sectionas independent parallel circuits. So, the total resistance is given by

$\begin{matrix}{R_{tot} = \left( {\sum\limits_{m = 1}^{M}\frac{1}{R_{m}}} \right)^{- 1}} & (17)\end{matrix}$

FIGS. 25A and 25B illustrate a first example embodiment with an inputprofile and output profile. The input profile has N dopant optimizedlateral dopant (OL=1.1 dB/cm) and two doping levels. The inputresistance is 8.5 □/segments, and the output resistance is 17.7□□segments. Two levels of the longitudinal profile are used to implementthis optimized lateral profile, but this is not good enough. However,the non-optimized resistance of a current modulator is 15□. Thus, theperformance of this output profile is close to a three-levelnon-optimized lateral profile.

FIGS. 26A and 26B illustrate a second example embodiment with an inputprofile and output profile. The input profile has N dopant optimizedlateral dopant (OL=1.1 dB/cm) and three doping levels. The inputresistance is 8.5 □/segments, and the output resistance is 10.2□□segments. The actual non-optimized resistance is 15□. Thus, using athree-level longitudinal profile to implement an optimized lateralprofile provides significant improvement.

FIGS. 27A and 27B illustrate a third example embodiment with an inputprofile and output profile. The input profile has N dopant optimizedlateral dopant (OL=1.1 dB/cm) and four doping levels. The inputresistance is 8.5 □/segments, and the output resistance is 8.9□□segments. Thus, this output profile has a resistance almost identicalto the input profile. It can be concluded that as the number of dopinglevels increase, the output profile access resistance tends to the valueof the input profile. However, a significant gain can already beobtained with three doping levels. Similar simulations were obtainedwith P-type dopant.

FIGS. 28A and 28B illustrate a fourth example embodiment with an inputprofile and output profile. The input profile has N dopant optimizedlateral dopant (OL=0.92 dB/cm) and two doping levels. The inputresistance is 16.1 □/segments, and the output resistance is 28.9□□segments. Here, using two levels of the longitudinal profile toimplement an optimized lateral profile is not good enough. However, thenon-optimized resistance of a current modulator is 26□. Thus, theperformance of this output profile is close to a three-levelnon-optimized lateral profile.

FIGS. 29A and 29B illustrate a fifth example embodiment with an inputprofile and output profile. The input profile has N dopant optimizedlateral dopant (OL=0.92 dB/cm) and three doping levels. The inputresistance is 16.1 □/segments, and the output resistance is 18.8□□segments. The actual non-optimized resistance is 26□. Thus, usingthree levels of the longitudinal profile to implement an optimizedlateral profile provides significant improvement.

FIGS. 30A and 30B illustrate a sixth example embodiment with an inputprofile and output profile. The input profile has N dopant optimizedlateral dopant (OL=0.92 dB/cm) and four doping levels. The inputresistance is 16.1 □/segments, and the output resistance is 16.9□□segments. The output profile has a resistance almost identical to theinput profile.

Again, an optical modulator could be significantly improved byoptimizing the lateral dopant profiles. Such profiles might, however,require process development effort. It has been shown that a customlateral implantation profile could be implemented using a longitudinalvariation of the dopant without degrading the other figure-of-merits ofthe optical modulator (optical losses, Vπ and EO bandwidth) since theaccess resistance is kept the same (when the number of doping level are>2).

This approach is thus beneficial in two situations: 1) to improve themodulator performances by mimicking more complex lateral profile havinglower access resistance while keeping the fabrication process simple,and 2) to keep the performance of the modulator as they are with onlytwo doping levels.

FIG. 31 illustrates a top view of another embodiment of a longitudinallyvarying profile. Again, it is shown using longitudinal variations of thedoped area to replicate various lateral doping profiles.

FIGS. 32A and 32B illustrate graphs of N (FIG. 32A) and P (FIG. 32B)dopants illustrating optical losses as a function of resistance persegment. The optimization process has also been run on another slabthickness. The other slab thickness is 150 nm (line 81) (it was 90 nm inthe previous examples (line 80)). A thicker slab has a lower accessresistance, but, at the same time, the optical mode is less confined inthe center part of the waveguide. As a result, the optical loss islarger. Before running this optimization process, it was not clear whichof the two aspects was dominating. As seen in FIGS. 32A and 32B, it isclear now that a thinner slab is more advantageous.

Reduction of Silicon Modulator Access Resistance with Silicon SlabThickness Optimization

In one or more embodiments, instead of having a slab-shaped transitionzone 2 with a uniform thickness along the longitudinal/lateraldirection, the transition zone 2 may be designed to have varyingthickness. More specifically, in the second example, the slab thicknessis varied on each side of the modulator to reduce the contact resistanceof the overall structure. FIGS. 33A, 33B, 34A, and 34B show, incross-section, various configurations for varying the slab thickness inaccordance with one or more embodiments disclosed herein. Otherconfigurations are possible, for example, thickness variation in thelongitudinal direction (not shown). For clarity, different thicknessvariations can be employed in either lateral and longitudinal directionsor in both directions (not shown).

FIGS. 33A and 33B show configurations where the slab thickness isincreased close to the electrodes with two and three silicon thicknesslevels respectively. In these cases, the resistance of the N+/P+ regions2 is decreased by a factor of two assuming a uniform doping profilewhich will translate into a modulator bandwidth improvement. In someconfigurations, the reduction of the contact resistance by ˜10Ω willimprove the modulator bandwidth by ˜5 GHz, such improvement is notnegligible. These configurations do not significantly modify the opticalmode profile and the effective index compared to the modulator shown inFIG. 1A-1C because the etching of the silicon layers (which defines thewaveguide) is wide enough to confine the optical mode (typically˜200-300 nm).

FIGS. 34A and 34B show other configurations where the transition zone 2(the region where the optical mode is exponentially decaying) beginswhere the silicon layer is still thick approaching the thickness of thewaveguide. Typically, such optical waveguide will support more than onepropagating mode. These configurations are particularly interestingbecause the thin transition zone 2 (which confines the optical modes) isonly composed of highly doped silicon. As a result, the sections wherethe resistance is the highest in FIG. 1 (i.e., the thin P/N dopedsections) are completely removed which considerably reduces the contactresistance. Further, optimization of this design may be undertaken toprevent higher order mode excitation, for example by adiabaticallycoupling into the first propagation mode or by adjusting the dopantprofiles to selectively attenuate the high order propagation modes.

The thickness variation of the transition zone 2 may be chosen such thatits longitudinal average agrees with the optimum lateral doping profiledescribed herein. In accordance with the second example, modifying theslab thickness allows one to reduce the contact resistance of theoverall structure even more without significantly degrading thepropagation losses. Reducing the contact resistance is important toreach higher modulation bandwidth.

For the purpose of illustration, the thickness variation is shown to beright-angled steps in FIGS. 33A-33B and 34A-34B. Nevertheless, it wouldbe readily appreciated by one skilled in the art that other shapes ofthickness variation, such as straight-line slopes, curvy-line slopes, orthe combination thereof, may also be used.

For the purpose of illustration, FIGS. 33A-33B and 34A-34B only depictone and two changes in thickness, respectively. Nevertheless, it wouldbe readily appreciated by one skilled in the art that the number ofthickness changes may be greater than 3. Further, FIGS. 33A-33B and34A-34B illustrate how to reduce the contact resistance of a siliconmodulator using a lateral PN junction as an example. However, it wouldbe readily appreciated by one skilled in the art that the techniquedescribed above in the second example may be applied to other types ofjunction geometries.

Further, in one or more embodiments, a silicon modulator may be designedto combine the features of the first example and the second example, sothat the transition zone 2 has both a varying longitudinal/lateraldoping concentration and a varying longitudinal/lateral thickness. Sucha combination of features from the two examples may decrease the contactresistance even further for a given optical loss.

Silicon Slab Thickness Optimization—Quantified

The thickness of the slab area for the transition zone 2 can be variedto improve the access resistance of the modulator while maintaining theoptical losses constant. Conversely, the thickness of the slab area canbe varied to improve the optical loss of the modulator for a specificaccess resistance. This is similar to the optimizations described hereinfor the lateral and longitudinal profiles.

To evaluate the above statements, the optical mode profile wascalculated and the fraction of power inside the slab and inside the coreof the waveguide was calculated. If the optical power in the slab issmaller, it means that the silicon can be doped more heavily withsmaller impact on the optical mode which results in either a fastermodulator or a modulator with lower optical losses. A full modulatorsimulation was also performed. The figure of merits of the modulator(optical losses, Vpi and EO BW) are compared to a legacy modulator.

With proper thickness choices, using a slab waveguide in the transitionregions 2 with notches on the side allows an improvement in the modeconfinement, a reduction of the optical power concentrated inside theslab area, and, as a result, the modulator performances can besignificantly improved. The actual designs show an improvement between 2GHz and 3 GHz. Considering the limited improvement that can be made onSi based modulator, a few GHz improvement can be the difference betweena working chip or a “failed chip.”

Optical Mode Profile Evaluation

FIGS. 35-38 are cross-sectional diagrams of various modulators with thewaveguide core 1 and the transition regions 2 and associated calculatedoptical mode illustrating different slab thicknesses in the transitionregions 2. FIG. 35 is a baseline modulator with no slab thicknessesvariations in the transition regions 2. The cross-sectional diagramincludes the waveguide core 1 and the transition regions 2 and acladding 80, such as a SiO₂ cladding. In an embodiment, the waveguidecode 1 is 220 nm thick and 500 nm wide; the slab in the transitionregions 2 has a thickness of 90 nm. The optical mode is used tocalculate the Poynting vector. The important values for this baselinemodulator are the fraction of the mode in the 500 nm×220 nm core (72.1%)and the portion of the mode inside the slab (3.8%).

FIG. 36 includes a transition region 2 with the slab thickness varied ontwo levels. The thin slab is 90 nm and the thick slab is 150 nm. Here,it is seen that the optical mode is slightly less confined (71.3%instead of 72.1%), but the amount of optical power inside the slab iseven larger than the baseline (4.3% instead of 3.8%). The amount ofoptical power can be made equal to the baseline in the slab byincreasing the value Δw. However, Δw is too large and this new waveguidegeometry does not provide access resistance benefit. As a result, thisapproach was not so useful.

FIG. 37 includes a transition region 2 with the slab thickness varied ontwo levels, but with smaller thicknesses from FIG. 36 . Specifically,the thin slab is 50 nm and the thick slab is 90 nm. Here, it is seenthat the optical mode is more confined (76.2% instead of 72.1%), but,more importantly, the amount of optical power inside the slab is muchlower (0.7% instead of 3.8%). This is able to improve the EO bandwidthof the modulator while involving relatively simple process changes.

FIG. 38 includes a transition region 2 with a varied geometry from FIG.37 , namely Δw is much smaller while the thicknesses are the same fromFIG. 37 . Here, it is seen that the optical mode is still more confined(74.7% instead of 72.1%) compared to the baseline, but less than theprevious case in FIG. 37 . More importantly, the amount of optical powerinside the slab is still much lower than the baseline (1.2% instead of3.8%).

Full Modulator Simulation

FIG. 39 shows a reference modulator and a second modulator utilizingvarious slab thicknesses in the transition region 2 (structure shown inFIG. 38 ). The modulator using various slab thickness has the same phaseresponse (same Vpi) and OL as the baseline modulator that uses a uniform90 nm thick slab. However, the access resistance is smaller for the sameoptical loss which results in this example in a 2 GHz improvement in theEO bandwidth. To match both modulators, the implantation recipes and themask position of these layers were finely tuned.

Although the present disclosure has been illustrated and describedherein with reference to preferred embodiments and specific examplesthereof, it will be readily apparent to those of ordinary skill in theart that other embodiments and examples may perform similar functionsand/or achieve like results. All such equivalent embodiments andexamples are within the spirit and scope of the present disclosure, arecontemplated thereby, and are intended to be covered by the followingclaims.

What is claimed is:
 1. A silicon-based modulator comprising: a waveguideincluding a contact region and a core region, wherein the waveguideincludes a dopant concentration that decreases from the contact regionto the core region in a transition zone according to a doping profilethat is variable, wherein the core region is weakly doped relative tothe transition zone and includes no variable doping therein.
 2. Thesilicon-based modulator of claim 1, wherein the doping profile is anexponential curve.
 3. The silicon-based modulator of claim 1, whereinthe doping profile includes a non-linear transition from the contactregion to the core region.
 4. The silicon-based modulator of claim 1,wherein the waveguide further includes a first region adjacent to thecontact region in a lateral direction within the waveguide; and a secondregion adjacent to the core region in the lateral direction within thewaveguide, wherein the doping profile decreases faster in the firstregion than in the second region.
 5. The silicon-based modulator ofclaim 1, wherein the transition zone includes a same thickness betweenthe contact region and the core region.
 6. The silicon-based modulatorof claim 1, wherein the transition zone includes a different thicknessbetween the contact region and the core region.
 7. The silicon-basedmodulator of claim 6, wherein the different thickness is varied indiscrete levels.
 8. The silicon-based modulator of claim 6, wherein thedifferent thickness is varied in any of right-angled steps,straight-line slopes, curvy-line slopes, and a combination thereof. 9.The silicon-based modulator of claim 1, wherein the transition zoneincludes a step at one or more of the core region and the contactregion.
 10. The silicon-based modulator of claim 1, wherein a thicknessof the transition zone is set such that highly doped silicon is inregions of smaller thickness.
 11. A method comprising: forming asilicon-based modulator that includes a waveguide including a contactregion and a core region, wherein the waveguide includes a dopantconcentration that decreases from the contact region to the core regionin a transition zone according to a doping profile that is variable,wherein the core region is weakly doped relative to the transition zoneand includes no variable doping therein.
 12. The method of claim 11,wherein the forming includes implanting of strong dopants in the contactregion, annealing and diffusing of the strong dopants, implanting ofweak dopants in the core region, and annealing and diffusing of the weakdopants.
 13. The method of claim 11, wherein the doping profile is anexponential curve.
 14. The method of claim 11, wherein the dopingprofile includes a non-linear transition from the contact region to thecore region.
 15. The method of claim 11, wherein the waveguide furtherincludes a first region adjacent to the contact region in a lateraldirection within the waveguide; and a second region adjacent to the coreregion in the lateral direction within the waveguide, wherein the dopingprofile decreases faster in the first region than in the second region.16. The method of claim 11, wherein the transition zone includes a samethickness between the contact region and the core region.
 17. The methodof claim 11, wherein the transition zone includes a different thicknessbetween the contact region and the core region.
 18. The method of claim17, wherein the different thickness is varied in discrete levels. 19.The method of claim 17, wherein the different thickness is varied in anyof right-angled steps, straight-line slopes, curvy-line slopes, and scombination thereof.
 20. The method of claim 11, wherein the transitionzone includes a step at one or more of the core region and the contactregion.